determine whether the equation defines y as a function of x? x^2 + 8y^2=1

Question

anonymous · Answer

can someone help me?

anonymous · Answer

thanks!

turingtest · Answer

The equation as it is is not defined in terms of x explicitly.
Are we allowed to change it?

turingtest · Answer

...as you have the equation right now it isn't in the form
y=(something)
so are we allowed to change it to answer your question?
I'm unclear.

earthcitizen · Answer

$$ x^2 + 8y^2=1$$

earthcitizen · Answer

solve implicitly

earthcitizen · Answer

$$(dy(x))/(dx) = -x/(8 y)$$

earthcitizen · Answer

$$(dx(y))/(dy) = -(8 y)/x$$

turingtest · Answer

there is no derivative in this problem @earth

earthcitizen · Answer

it looked like an implicit function

turingtest · Answer

if y is supposed to be defined in terms of x it isn't.
if we have to solve for y we wind up taking a +/- square root, so th graph would fail the vertical line test.
it looks to me like that is all needed to say that this is not a function. at least not as it is.

earthcitizen · Answer

is ut a circle equation ?

turingtest · Answer

right, and a circle fails the vertical line test
so no, not a function I say.

turingtest · Answer

sorry, not a circle, an ellipse

turingtest · Answer

still not a function

jhonyy9 · Answer

- so i think it like :

y=f(x)=+/- sqrt((1-x2)/8)